1. Transforming energy with magnetism
Magnetic Induction
Transforming energy with magnetism

2. Lorentz Force Reminder
F = qv  B
Source: Griffith, The Physics of Everyday Phenomena
F is directed out of the screen.

3. CPS Question
What is the direction of the Lorentz force on the charges moving in this wire? B A. D. B. E. C. F. I

4. Current in a Field Feels a ForceB F I

5. Circuit in a Field Has TorqueB I I

6. Torque Turns a Motor I
current I
force F B

7. Moving Creates an EMF – B v +
induced potential

8. Notice the direction B I A current moved the wire
The motion created an emf opposing the current that initiated it!

9. Moving conductor Each charge receives a force qvB
Conductor becomes polarized
Potential inside a conductor!?

10. Moving conductor Force F = qvB Work w = (qvB)·L
Potential e = (vB)·L
Notice:
L  v and L  B
so, L || vB
Optimal orientation!

11. Why “EMF”? It definitely is electromotive
It’s not a force. Units V = J/C
Not a potential: not a conservative force
So we just call it “emf,” never mind the origin

12. Aside: Scalar Triple Product
(A  B)  C
volume of parallelepiped defined by A, B, C
Equivalent to
(B  C)  A
(C  A)  B B A C

13. Rotating Loop Creates CurrentB V V

14. Rotating Loop Creates CurrentB V V

15. Rotation Powers a Generatorv
Motion B
through the field V
induces a potential
which generates a current
that charges the battery

16. Magnetic Flux Field through a surface F = BA
Effectively the number of field lines enclosed by a loop

17. Group Work a b c d e
At which position(s) does the most magnetic flux pass through the loop?
At which position(s) is the magnetic flux through the loop changing the fastest?

18. Flux Change Creates Emf
Faraday’s Law
Changing the magnetic flux through a loop creates an emf around the loop.
e =
–DF Dt

19. Magnetic Flux Flux changes as loop turnsb c d e
Flux changes as loop turns
At a, c, e: Greatest flux F, least change
At b, d: Zero flux, fastest flux change DF/Dt

20. Induced current direction
Lenz’s Law
The current induced by changing the magnetic flux inside a circuit generates a magnetic field that opposes the change.

21. Lenz’s Law Explains Generator
changing field e
opposing field B
needed I

22. Group Work
What is the Lorentz force on each side?
Which direction is the flux change?
What current would oppose it? B
If the loop inside this magnetic field expands, in what direction will the induced current be?

23. Group Work
Which direction is the flux change?
What current would oppose it? B
If the magnetic field becomes weaker, in what direction will the induced current be?

24. How a Microphone Works microphone geophone
Flux inside loop becomes more

25. Wave-Powered Generator
Originally appeared in Smithsonian magazine.

26. How a Loudspeaker Works
induced motion of magnet
current-generated field attracts or repels magnet
current

27. AC Transformers
Source: OSHA

28. Flux Change Creates Emf
Rapidly changing field
high induced emf
unchanging field
zero induced emf

29. How a Transformer Works
AC current in the primary coils creates a changing magnetic field.
The magnetic flux inside the secondary coils changes
Changing flux induces emf in the secondary coils

30. Potential Proportional to Loops
Same flux F through both sets of windings
Each loop adds emf
Emf’s V are proportional to the number of loops N V1 N1 V2 N2 =

31. Energy is Conserved Ideally: power in = power out V1I1 = V2I2
Realistic: power in > power out
Efficiencies usually around 95%

32. Transformer Summary Power in  power out  loops  higher V, lower I
 loops  lower V, higher I

33. Question
A “step-down” transformer converts input at 120 V to output at 20 V. If the input circuit has 1100 W, how much power is available at the output?
200 W.
660 W.
1100 W.
2400 W.

34. General Physics L18_Faraday
Group Work
A transformer with 1000 primary windings converts AC at 110 V (primary) to 220 V (secondary).
Which is greater: the voltage in the primary circuit or the voltage in the secondary circuit?
Where will the number of loops be greater: in the primary or in the secondary?

35. Group Work
A transformer with 1000 primary windings converts AC at 110 V (primary) to 220 V (secondary).
What is the voltage ratio V2/V1?
What is the loops ratio N2/N1?
How many loops are in the secondary circuit (N2)?

36. Group Work
A transformer with 1000 primary windings converts AC at 110 V (primary) to 220 V (secondary).
What is the current ratio I2/I1?

37. Formulas for Transformers
Loops: V1 V2 N1 N2 =
Power: V1I1 = V2I2
Potential: V2 = V1 I1 I2
= V1 N2 N1
Current: I2 = I1 V1 V2
= I1 N1 N2

38. Example
A transformer with 5000 primary coils and 100 secondary coils has an input voltage of 50 kV. What is the output voltage?
Vout = Vin Nout/Nin
= (50 kV)(100/5000)
= (50 kV)/50
= 1 kv = 1,000 V